Implementing Quantum Secret Sharing on Current Hardware

Quantum secret sharing is a cryptographic scheme that enables the secure storage and reconstruction of quantum information. While the theory of secret sharing is mature in its development, relatively few studies have explored the performance of quantum secret sharing on actual devices. In this work, we provide a pedagogical description of encoding and decoding circuits for different secret sharing codes, and we test their performance on IBM's 127-qubit Brisbane system. We evaluate the quality of the implementation by performing a SWAP test between the decoded state and the ideal one, as well as by estimating how well the code preserves entanglement with a reference system. The results indicate that a ((3,5)) threshold secret sharing scheme and a non-threshold 7-qubit scheme perform similarly based on the SWAP test and entanglement fidelity, with both attaining a roughly 70-75% pass rate on the SWAP test for the reconstructed secret. We also investigate one implementation of a ((2,3)) qutrit threshold scheme and find that it performs the worst of all, which is expected due to the additional number of multi-qubit gate operations needed to encode and decode qutrits. A comparison is also made between schemes using mid-circuit measurement versus delayed-circuit measurement.